arithmetic-geometric series

The general arithmetic-geometric series of n terms is a series of the form:

a + (a+d)r + (a + 2d)r^2 + ... +[a + (n - 1)d]r^n-1 Where the first factors of each term form an arithmetic series and the second factors form a geometric series. What technique could I use to derive a formula for the sum of this series? Could I let S denote the sum of the general geometric series of n terms. Multiply S by r and write the series corresponding to the difference between S and rS. How would I use this expression to deducde the formula for the sum of the general geometric series? :eek: